Advanced Algebra-Chp 2-1-2-5 - Fall 2015

Front 1

State the domain and range of the relation: [(0.5,3), (0.4, 2), (3.1, 1), (0.4, 0)]

Back 1

domain: 0.5, 0.4, 3.1

range: 3, 2, 1, 0

Front 2

Definition of a function.

Back 2

Relation where every input has a unique output.

Front 3

Find the value of f(12) if f(x) = -2x + 4

Back 3

f(12) = -20

Front 4

Back 4

g(-2) = 6

Front 5

Find the value of h(3c) if h(x) = 2x - 1

Back 5

h(3c) = 6c - 1

Front 6

Back 6

1) domain = all real numbers between 0 and 10

range = all real numbers between -2 and 8

2) It is not a function because every input DOES NOT have a unique output.

Front 7

Give an example of the vertical line test. Explain your example.

Back 7

Front 8

Graph the relation y = 3.

(No calculator)

Back 8

Front 9

Graph the relation y = 3x + 2

(No Calculator)

Back 9

Front 10

Graph the relation x = -4

(No Calculator)

Back 10

Front 11

The number of students N in Cassia's school is given by N = 120 + 30G, where G is the grade level (for example 1st grade, 2nd grade, etc.).

1) Is 285 in the range of the function?

2) Explain your answer.

3) Is this function discrete or continuous? Explain.

Back 11

1) No

2) If you solve for G the answer is G = 5.5 but grade levels are integers so G is not in the range of the function.

3) This is a discrete functions because grade levels are integers.

Front 12

Back 12

Yes, because it can be rewritten as

f(x) = -1/5(x) + 0.2 which is slope intercept form of a linear equation. The exponents of all the variables is equal to 1.

Front 13

Is 2x + xy - 3y = 0 a linear function?

Explain your answer.

Back 13

It is not linear because the variables x and y are multiplied together.

Front 14

Back 14

It is not linear because the variable is in the denominator which means it has a negative exponent. Therefore the exponent of the variable is not 1.

Front 15

Back 15

It is not linear because the exponent of the variable is not 1.

Front 16

Clearly identify the x and y intercepts of the equation and then graph the function.

2x - 7y = 14

Back 16

Front 17

Write the equation in standard form:

2x = 4y -1

Back 17

2x - 4y = -1

Front 18

Paul charges people $25 to test the air quality in their homes. The device he uses to test air quality cost him a one charge fee of $500.

1) Write an equation that describes Paul's net profit (P) in terms of number of clients(c).

2) How many clients does he need to break even?

Back 18

1) P = 25c - 500

2) At break even P = 0 so:

0 = 25c - 500

500 = 25c

20 = c

He needs to have 20 clients to break even.

Front 19

During a camping trip in the North Woods in Canada, acouple went one-third of the way by boat, 10 miles by foot,and one-sixth of the way by horse. How long was the trip?

Back 19

20 miles

Front 20

What does slope measure on a graph of a linear equation?

Back 20

The steepness of the line.

Front 21

Back 21

140 meters/minute or ~.07 minutes per meter

Front 22

Find the slope of the line that passes through the points (4, 7) and (-6, -6). Express as a fraction in simplest form.

Back 22

13/10

Front 23

Sketch a graph for each of the following cases. Clear identify the graphs.

1) a line with a positive slope

2) a line with a negative slope

3) a line with a 0 slope

4) a line with a undefined slope

Back 23

Front 24

Naomi left from an elevation of 7400 feet at 7:00 A.M. and hiked to an elevation of 9800 feet by 11:00 A.M. What was her rate of change in altitude per hour? (simplified)

Back 24

600 feet/hour

Front 25

Write an equation in slope intercept form for the line that passes through the point (3, 7) with a slope of -2.

Back 25

y = -2x + 13

Front 26

Write an equation in point-slope form that has a slope of 4 and passes through the point (-2, 5)

Back 26

y - 5 = 4(x + 2)

Front 27

Write an equation in slope-intercept form that has a slope of 1/3 and an x-intercept of 5.

Back 27

y = (1/3)x - 5/3

Front 28

Write an equation in slope-intercept form that is perpendicular to y = (-1/2)x + 3 and passes through the point (8,2)

Back 28

y = 2x - 14

Front 29

Write an equation in slope-intercept form that is parallel to y = 3x + 1 and passes through the point (-1, 5)

Back 29

y = 3x + 8

Front 30

Write the equation in slope-intercept form that passes through (-2, -4) and (1, 8)

Back 30

y = 4x + 4

Front 31

Back 31

y = -3x + 5

Front 32

Back 32

y = -6

Front 33

Back 33

y = (4/3)x + 11/3

Front 34

Back 34

x = 3

Front 35

The surface of Grand Lake is at an elevation of 648 feet. During the current drought, the water level is dropping at a rate of 3 inches per day. If this trend continues, write an equation that gives the elevation in feet of surface of Grand Lake after x days.

Back 35

y = -3x + 648

Front 36

Find the value of r such that the line that passes through the two points has a slope of 1/3.

(8, 1), (5, r)

Back 36

r = 0

Front 37

Back 37

1) no correlation

2) There is no relationship between the colors in the rainbow and shoe size

Front 38

Back 38

1) Positive correlation

2) The more time spent studying the higher the student grade

Front 39

Back 39

1) negative correlation

2) The more time spent training the faster one can run 100 meters.

Front 40

Back 40

Sample answer:

1) y = (10/3)x - 20/3

2) ~8.88

Front 41

Back 41

y = 2.01x - .86